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Dual truncated Toeplitz operators [PDF]

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuanhao Ding
exaly   +3 more sources

Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball [PDF]

Acta Mathematica Sinica, English Series, 2011
Let \(A^2_{\alpha}(B_n)\) be the standard weighted Bergman space over the unit ball \(B_n\) in \(\mathbb{C}^n\), and let \(P_{\alpha}\) be the corresponding Bergman projection. For a function \(f \in L^{\infty}(B_n)\), the dual Toeplitz operator is defined by \(S_fu = (I-P_{\alpha})(fu)\), for \(u \in (A^2_{\alpha}(B_n))^{\perp}\).
Yu Feng Lu, Lu Yu Feng
exaly   +3 more sources

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(Asymmetric) Dual Truncated Toeplitz Operators

Trends in Mathematics, 2022
Multiplication operators on the space L2(T) on the unit circle T with Lebesgue measure are classical operators. So are Toeplitz operators on the Hardy space H2⊂L2(T). Sarason’s paper (Oper Metrices 1:491–526, 2007) has started investigations of truncated Toeplitz operators (TTO), i.e., compressions of these multiplication operators to model spaces.
Cristina Camara, Marek Ptak, Kamila Kliś-Garlicka   +2 more
exaly   +3 more sources

Commuting Dual Toeplitz Operators on the Polydisk

Acta Mathematica Sinica, English Series, 2006
Let \(\Omega\) be a bounded domain in \(\mathbb C^n\) and let \[ P:L^2(\Omega,dv)\to L^2_a(\Omega,dv) \] denote the Bergman projection, where \(L^2_a(\Omega,dv)\) is the Bergman space consisting of holomorphic functions in \(L^2(\Omega,dv)\). For a bounded function \(\varphi\) on \(\Omega\), the dual Toeplitz operator \(S_\varphi\) is the bounded ...
Yu Feng Lu, Lu Yu Feng
exaly   +3 more sources

Dual Toeplitz operators on the sphere

Acta Mathematica Sinica, English Series, 2013
The paper is devoted to the systematic study of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in \(\mathbb{C}^n\). A criterion of commutativity of two dual Toeplitz operators is obtained. A criterion guaranteeing that the product of two dual Toeplitz operators is again a dual Toeplitz operator is also ...
Hocine Guediri
exaly   +3 more sources

Dual Toeplitz Operators on the Sphere Via Spherical Isometries

Integral Equations and Operator Theory, 2015
Let \(\mathbb{B}_n\) be the open Euclidean unit ball in \(\mathbb{C}^n\), \(\mathbb{S}_n=\partial\mathbb{B}_n\) its boundary and \(\sigma\) the normalized surface measure on \(\mathbb{S}_n\). Given \(\varphi\in L^\infty(\sigma)\), the Toeplitz operator \(T_\varphi\) with symbol \(\varphi\) is defined as the compression of the multiplication operator ...
Jörg Eschmeier, Eschmeier Jörg
exaly   +3 more sources

Invertibility and spectral properties of dual Toeplitz operators

Journal of Mathematical Analysis and Applications, 2020
Consider \(L_2(\mathbb{D})\), where \(\mathbb{D}\) is the unit disk on the complex plane, and its Bergman subspace \(L^2_a\) consisting of analytic functions. Let \(P\) be the orthogonal projection of \(L_2(\mathbb{D})\) onto \(L^2_a\). Given \(\varphi \in L^{\infty}(\mathbb{D})\), the dual Toeplitz operator \(S_{\varphi}\) with symbol \(\varphi\) is ...
Xuanhao Ding
exaly   +3 more sources

Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

Acta Mathematica Sinica, English Series, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng, Yang, Zhao, Xian Feng
exaly   +3 more sources

Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space

Acta Mathematica Sinica, English Series, 2009
Let \(D\) be the open unit disk in the complex plane and let \(dA\) denote the normalized Lebesgue measure. The Sobolev space \(W^{1,2}\) consists of functions \(u:D\to\mathbb{C}\) with the weak partial derivatives of order 1 and the norm \[ \|u\|_{\frac{1}{2}}=\left(\left|\int_D u dA\right|^2+\int_D\left(\left|\frac{\partial u}{\partial z}\right|^2 ...
Tao Yu
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Block dual Toeplitz Operators on the Orthogonal Complements of Fock Spaces

Acta Mathematica Sinica, English Series
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yu Feng Lu, Lu Yu Feng
exaly   +3 more sources